MC SCF molecular gradients and hessians: Computational aspects

Molecular gradients and hessians for multiconfigurational self-consistent-field wavefunctions are derived in terms of the generators of the unitary group using exponential unitary operators to describe the response of the energy to a geometrical deformation. Final expressions are cast in forms which contain reference only to the primitive non-orthogonal atomic basis set and to the final orthonormal molecular orbitals; all reference to intermediate orthogonalized orbitals is removed. All of the deformation-dependent terms in the working equations reside in the one- and two-electron integral derivatives involving the atomic basis orbitals. The deformation-independent terms, whose contributions can be partially summed, involve symmetrized density matrix elements which have the same eight-fold index permutational symmetry as te one- and two-electron integral derivatives they multiply. This separation of deformation-dependent and -independent factors allows for single-pass integral-derivative-driven implementation of the gradient and hessian expressions.